Unit 8, Lesson 6
Finding Side Lengths of Triangles
Accelerated 7
Preparation
Lesson Narrative
In this lesson students investigate relationships between the side lengths of right and non-right triangles, leading to the Pythagorean Theorem.
Students begin by comparing aspects of 4 triangles purposefully chosen to prime them to think about patterns. In the next activities, students notice patterns between the side lengths of right and non-right triangles and the areas of squares that share a side length with the right and non-right triangles (MP8). Students learn that the legs of a right triangle are the sides that make the right angle and the hypotenuse is the side of a right triangle that is opposite the right angle. By the end of this lesson, they see that for right triangles only, given legs and and hypotenuse , the side lengths are related by . In the next lesson they will prove this, better known as the Pythagorean Theorem.
- Comprehend the term “Pythagorean Theorem” (in written and spoken language) as the equation $a^2+b^2=c^2$, where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse of a right triangle.
- Describe (orally) patterns in the relationships between the side lengths of triangles.
- Determine the exact side lengths of a triangle in a coordinate grid and express them (in writing) using square root notation.
Let’s find triangle side lengths.
Required Preparation
None
The hypotenuse is the side of a right triangle that is opposite the right angle. It is the longest side of a right triangle.
Here are some right triangles. Each hypotenuse is labeled.
The legs of a right triangle are the sides that make the right angle.
Here are some right triangles. Each leg is labeled.
The Pythagorean Theorem describes the relationship between the side lengths of right triangles.
The square of the hypotenuse is equal to the sum of the squares of the legs. This is written as .
This diagram shows the relationship.